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Question
Select the correct option from the given alternatives:
Given A = `[(1, 3),(2, 2)]`, I = `[(1, 0),(0, 1)]` if A – λI is a singular matrix then _______
Options
λ = 0
λ2 – 3λ – 4 = 0
λ2 + 3λ – 4 = 0
λ2 – 3λ – 6 = 0
Solution
Given A = `[(1, 3),(2, 2)]`, I = `[(1, 0),(0, 1)]` if A – λI is a singular matrix then λ2 – 3λ – 4 = 0
Explanation:
Since A – λI is a singular matrix,
A – λI = 0
`[(1, 3),(2, 2)] - λ[(1, 0),(0, 1)] = 0 `
`[(1, 3),(2, 2)] - [(λ, 0),(0, λ)] = 0`
`[(1 - λ, 3),(2, 2 - λ)] = 0`
∴ (1 – λ) (2 – λ) – 6 = 0
∴ 2 − λ − 2λ + λ2 − 6 = 0
∴ 2 – 3λ + λ2 – 6 = 0
∴ λ2 – 3λ – 4 = 0
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